Abstract

The tunneling of electromagnetic waves in the band-gap region of periodic dielectric arrays is investigated with the coherent microwave transient spectroscopy technique. Transmission probabilities at frequencies in the fundamental band gap are measured and found to depend exponentially on sample thickness. From these results the frequency dependence of the imaginary wave vector is determined. The peak imaginary wave vector, which occurs at midgap, is observed to be proportional to the width of the band gap, unlike the case for single-barrier tunneling of electrons, where the relationship is expected to vary as the square root of the barrier height.

In a periodic dielectric medium, Maxwell's wave equation for electric displacement vector D, when expanded in terms of plane waves, contains three terms.8 They are the kinetic energy term (k + G)2, the potential energy term ∼V(G − G′), and the total energy term ω2/c2. Here, G is a reciprocal-lattice vector and c the speed of light. When ∊(r) is properly scaled, the corresponding wave equation can be expressed in terms of dimensionless constants, i.e., kao, Gao, and ωao/c. It follows that Eg at the Brillouin zone edge scales linearly with 1/ao as does κ at the midgap. Hence, a linear relationship between Eg and κmax is expected.

Other

In a periodic dielectric medium, Maxwell's wave equation for electric displacement vector D, when expanded in terms of plane waves, contains three terms.8 They are the kinetic energy term (k + G)2, the potential energy term ∼V(G − G′), and the total energy term ω2/c2. Here, G is a reciprocal-lattice vector and c the speed of light. When ∊(r) is properly scaled, the corresponding wave equation can be expressed in terms of dimensionless constants, i.e., kao, Gao, and ωao/c. It follows that Eg at the Brillouin zone edge scales linearly with 1/ao as does κ at the midgap. Hence, a linear relationship between Eg and κmax is expected.

Cited By

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.